This invention relates generally to holographic microscopy and more particularly to the numerical reconstruction of holograms.
Conventional optical, confocal or electron microscopes have certain limitations. High resolution conventional microscopes are costly and the resolution of such microscopes is limited by the physical imperfections inherent in lenses. Conventional optical and electron microscopes take only two dimensional images. Confocal microscopes allow three dimensional imaging but only in a horizontal plane and only the auto-florescent part of a sample can be seen. If staining is used to display other parts of the sample, the staining process kills most biological specimens. Finally, the focusing time required by conventional microscopes limits how rapidly successive images of a specimen may be taken.
Holography offers solutions to some of the inherent problems with conventional microscopy. Holographic microscopy using spherical wave fronts was first proposed by Denis Gabor in 1948. He sought to overcome the limitations inherent in the use of lenses. He introduced the concept of recording not only the intensity of the wave scattered by the sample being measured but also the wave""s phase. This phase information is used in a reconstruction process to reveal the three-dimensional shape of the sample being measured.
Whereas the limitation in optical microscopy is the quality of the lenses, the limitation in holographic microscopy has been the reconstruction process. Reconstruction can be either physical or numerical.
The method of reconstruction first suggested by Gabor was physical reconstruction of an in-line hologram. In in-line holography, the sample to be measured is situated close to a point source of radiation. A small fraction of the waves impinging on the sample are scattered by the sample. A hologram then results from the interference of the scattered wave and the unscattered reference wave coming directly from the source. This hologram is registered as a series of interference fringes on a photographic film in line with the point source and the sample. The reconstruction of the scattered wavefront, i.e. the xe2x80x9cimagexe2x80x9d of the sample, is then obtained by illuminating the hologram with a duplicate of the reference wave source.
There are problems with the physical method of reconstruction for in-line holography. In particular, the reconstructed image of the sample is dominated by the much brighter, out of focus, image of the point source, and is also blurred by a xe2x80x9cghostxe2x80x9d twin image. To overcome the problems of in-line holography various schemes of off-line holography have been developed. However, these methods introduce the use of lenses thereby reintroducing some of the problems sought to be overcome by holographic microscopy in the first place.
Another reconstruction method, which has been suggested to overcome the problems of in-line physical reconstruction, is numerical reconstruction. Numerical reconstruction methods commonly employ the Kirchhoff-Helmholtz reconstruction formula in various formulations. Because a phase factor in the Kirchhoff-Helmholtz formula is highly nonlinear in the spatial domain, in past applications various approximation schemes have been suggested, such as an on-axis Fraunhofer-type approximation and a range of weighting functions, to ultimately allow the use of multiple Fast-Fourier-Transforms (FFTs) for efficient high-speed reconstruction. A recent paper employing such approximations is E. Cuche et al., Applied Optics, 38 (1999) 6994-7001.
Most numerical reconstruction methods are unsatisfactory because the approximations used in the reconstruction methodology result in poor image quality. On the other hand, a full implementation of the Kirchhoff-Helmholtz reconstruction formula for high-resolution images requires inordinately long computation time so that any real-time implementation is out of the question. This non-real time numerical reconstruction limits the obtaining of images to post processing and does not allow for the adjustment of the measurement in response to the initial images.
The invention may be summarized according to a first broad aspect as a method of fast and accurate numerical reconstruction of large holograms, large enough to get maximum resolution, i.e. of the order of the wavelength of the radiation used. This is achieved by a nonlinear coordinate transformation of the Kirchhoff-Helmholtz formula to remove the non-linearity from the phase factor of the formula. This is followed by an image interpolation scheme to generate an equidistant intensity distribution to which FFT methods are applied. This is essentially an exact evaluation of the Kirchhoff-Helmholtz formula.
The invention may be summarized according to a another broad aspect as a practical scheme for the realization of a digital holographic microscope, which outlines the steps necessary to obtain maximum resolution, approaching the theoretical allowed maximum, including the real-time numerical reconstruction method.
Advantageously, the reconstructed image is of a higher quality, i.e. greater resolution, than those provided by previous numerical reconstruction methods.
Also advantageously, reconstruction can be conducted in real time so that adjustments may be made while the sample is still available and in position.
Additionally, the speed of processing permits rapid successive images to be viewed, which is particularly advantageous where the sample is an active biological specimen.
Further, the use of in-line holography enables the use of a simple, inexpensive apparatus and does not require staining or other treatments of biological specimens.
Finally, reconstruction can be truly three-dimensional allowing the reconstructed sample to be viewed from any direction and the structure of the specimen to be examined.
Other aspects and features of the invention will become apparent to those of ordinary skill in the art upon review of the following description of specific embodiments of the invention in conjunction with the accompanying figures.